Are you able to boot into the old proxmox. If so, please backup all your VM's, this makes moving the configuration around much easier.
No boot into your nvme instance, go to storage(Datacenter->Storage->Add) and add a LVM-thin, now you should be able to add your old disk on the side view.
When it's ready, click on the disk, and you should see VM disk Images and Backups and restore them.
But you can try testing it out yourselfe on proxmox.
1. Create a VM and install proxmox on it(don't forget to set the cpu type to host) and create a vm
2. Stop the Proxmox VM, go to hardware, detach the current disk and add a new one and install proxmox again on this VM, and attach the old disk again.
3. Now try to recover the old VM, but as this is a minimal setup and everything virtualized, nothing can go wrong